Question
Solve $x(x + 1) + (x + 2)(x + 3) = 42$
✓
Answer
$x(x + 1) + (x + 2)(x + 3) = 42$
$\Rightarrow x^2+x+x^2+3 x+2 x+6-42=0$
$\Rightarrow 2 x^2+6 x-36=0$
$\Rightarrow 2 x^2+12 x-6 x-36=0$
$\Rightarrow 2 x(x+6)-6(x+6)=0$
$\Rightarrow (x+6)(2 x-6)=0$
if $x + 6 = 0$ or $2x - 6 = 0$
then $x = -6$ or $x = 3$
$\Rightarrow x^2+x+x^2+3 x+2 x+6-42=0$
$\Rightarrow 2 x^2+6 x-36=0$
$\Rightarrow 2 x^2+12 x-6 x-36=0$
$\Rightarrow 2 x(x+6)-6(x+6)=0$
$\Rightarrow (x+6)(2 x-6)=0$
if $x + 6 = 0$ or $2x - 6 = 0$
then $x = -6$ or $x = 3$
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